WASHINGTON—A crucial Republican senator said he could accept a tax-policy framework that would let the GOP cut taxes by about $250 billion over the next decade and possibly hundreds of billions of dollars more, staking out a position that could help shape the party’s planned tax overhaul.

Sen. Bob Corker (R., Tenn.), a pivotal vote on the Senate Budget Committee, is framing the debate by defining his position on tax breaks that have already lapsed or are scheduled to expire in the coming years.